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September 17, 2025

A Fully Invertible Global Analytic Model of the Riemann Zeta Function

Key Points

The novel analytic framework shows that the zeta function does not vanish in any compact region away from the critical line.
Key evidence includes the establishment of behavior insights of zeta zeros independent of the Riemann Hypothesis.
The study constructs a specialized atomic system in the Hardy space H2(C+) to analyze the zeta function.
These findings highlight new theoretical avenues for understanding the distribution of the non-trivial zeros.

Abstract

This paper introduces a novel analytic framework to study the distribution of non-trivial zeros of the Riemann zeta function. By constructing a specialized atomic system in the Hardy space H2(C+), we prove that ζ(ρ) does not vanish in any compact region away from the critical line. This result provides new insights into the behavior of zeta zeros, independent of the Riemann Hypothesis.

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Sui Qing (Tue,) studied this question.

www.synapsesocial.com/papers/68d45b1b31b076d99fa5d7ac — DOI: https://doi.org/10.33774/coe-2025-0jbmf-v3

A Fully Invertible Global Analytic Model of the Riemann Zeta Function

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Abstract

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